EQUATIONS IN NONLINEAR ELLIPTIC PARTIAL DERIVATIVES THAT ARISE IN PHYSICS AND GEOMETRIA

Operation co-funded by EU cohesion policy (European Regional Development Fund (ERDF)) under the programme Multi-regional Spain - ERDF (2014ES16RFOP002), managing authority: Subdirección General de Gestión del FEDER, de la Dirección General de Fondos Europeos del Ministerio de Hacienda.. The source names no beneficiary for this operation. Location: Province of Granada (NUTS ES614); Spain. Budget: total eligible expenditure EUR 79,134; EU co-financing EUR 63,307.2 (co-financing rate 80%), as stated by the source. Runs 2019-01-01 to 2021-12-31. Source: Kohesio, EU cohesion policy projects managed by national and regional authorities (not CORDIS); selected because its summary names quantum technology. Summary from Kohesio (English machine translation by the source): THE PROJECT ¿NONLINEAR ELIPTIC PARTIAL DIFFERENTIAL EQUATIONS ARISING IN PHYSICS AND GEOMETRY¿ (PDEPHYS&GEOM) IS GUARANTEED BY THE PREVIOUS WORK IN THE PROJECT MTM2015-68210-P (IPS: D. ARCOYA AND D. RUIZ) AND WITH THE CORRESPONDING PROJECTS THAT OUR GROUP HAS CONTINUOUSLY DEVELOPED SINCE 1998. A BALANCE HAS BEEN SOUGHT BETWEEN THE CONSERVATION OF THE RESEARCH TRAJECTORY OF ITS MEMBERS (WHICH IS ACCREDITED BY THE QUANTITY AND QUALITY OF THE PREVIOUS PUBLICATIONS) AND THE REALIZATION OF NEW COMPETITIVE AND INTERESTING PROPOSALS IN WHICH THE CONFLUENCE OF DIFFERENT KNOWLEDGE AND TECHNIQUES ACQUIRED BY THE GROUP CAN GIVE RISE TO RELEVANT HIGHER RESULTS. THE OBJECTIVES OF THE PROPOSAL ARE DIVIDED INTO 4 LINES OF RESEARCH: 1. NONLINEAR ELLIPTIC PDES IN GEOMETRIC ANALYSIS: CURVATURE PRESCRIPTION PROBLEMS IN DOMAINS WITH BOUNDARY, OVERDETERMINED ELLIPTIC PROBLEMS, STABLE SOLUTIONS OF ELLIPTIC PROBLEMS. 2. NONLINEAR PDES IN QUANTUM MECHANICS: THE MOTION OF CHARGED PARTICLES IN ELECTROMAGNETIC FIELDS AND SPECIAL THEORY OF RELATIVITY, TRAVELING WAVES FOR THE GROSS-PITAEVSKII EQUATION. 3. NONLOCAL ELLIPTIC PROBLEMS: NONLOCAL PROBLEMS (FOR FRACTIONAL LAPLACIAN OPERATORS) WITH EITHER NEUMANN OR MIXED BOUNDARY CONDITIONS, NONLOCAL LIOUVILLE THEOREMS, NONLOCAL CONCENTRATION PHENOMENA. 4. QUASILINEAR PROBLEMS WITH LOWER ORDER TERMS DEPENDING ON THE GRADIENT AND SINGULARITIES. IN ORDER TO FACE THOSE QUESTIONS, WE SHALL USE TECHNIQUES COMING FROM NONLINEAR ANALYSIS: VARIATIONAL METHODS AND MIN-MAX, LERAY-SCHAUDER DEGREE, SINGULAR PERTURBATION METHOD, ETC. OTHER TOOLS FROM PDE¿S WILL ALSO BE OF USE, LIKE HOMOGENIZATION, BLOW-UP ANALYSIS, SUB- SUPERSOLUTIONS, MOVING PLANES, ETC. THE CONTRIBUTION OF THE FOREIGNER MEMBERS OF THE PROJECT, TOGETHER WITH THE REST OF INTERNATIONAL RELATIONS OF THE GROUP AND ITS RESEARCH BACKGROUND ARE REASONS TO CONCLUDE THE VIABILITY OF THIS AMBITIOUS PROJECT. TO THIS IT WILL CONTRIBUTE, ESPECIALLY IN THE RELATIONSHIP WITH PROBLEMS ARISING IN PHYSICS, THE [shortened; the full text is on the Kohesio page]

Original source.

Source: Kohesio (EU cohesion policy projects), European Commission, Directorate-General for Regional and Urban Policy (DG REGIO). Retrieved 2026-10-21. Licence: CC0 1.0 (Cohesion Open Data Platform, dataset 2014-2020 Kohesio projects). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: public domain dedication (CC0 1.0).

AI-assisted summary: The project "Nonlinear Elliptic Partial Differential Equations Arising in Physics and Geometry" is co-funded by the EU under the Multi-regional Spain programme, with a budget of EUR 79,134 and EU co-financing of EUR 63,307.2, running from January 1, 2019, to December 31, 2021. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.